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I'm analyzing a set of biological samples. Each sample is linked to a specific carbon and nitrogen concentration, representing the 2D (experimental) design space I referenced in the title. I've measured 20 metabolites for each sample. Initially, I used standard correlation/PCA analysis for this multivariate data. However, for this approach, I ignored the carbon/nitrogen coordinates. What methods can I employ to compare the samples while incorporating the C/N coordinates, i.e., the structure of the design space?

Here's n data table example: enter image description here

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    $\begingroup$ one approach would be to treat this as a spatial stats problem and use those tools. $\endgroup$ Sep 23, 2023 at 17:32
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    $\begingroup$ See this similar question for an approach using multivariate generalized additive models. $\endgroup$
    – EdM
    Sep 23, 2023 at 18:04
  • $\begingroup$ I think I grasped the main methods and I guess all the applicable methods are extension or generalisations of MANOVA. In the regression side, GLM would be the basic extension, and then it can get complex with GAM, hierarchical models and bayesian methods. If we consider a structure in the x, y coordinates, then spatial methods would be a complement: variogram, spatial autocorrelation, etc.. Finally, if we get structure in carbon/nitrogen and also in the measurements, maybe starting with simultaneous equation models and then SEM. There's another extension of MANOVA (chemometrics) called ASCA. $\endgroup$ Sep 25, 2023 at 11:32
  • $\begingroup$ I'll read more about it and compile everything into an answer, could be useful for other people in the future $\endgroup$ Sep 25, 2023 at 11:33

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